given the figure below solve for the value x

Question

Maquinanajames771go Maquinanajames771go

Math

Answered

given the figure below solve for the value x

Sagot :

Go Training: Other Questions

BaseDecimalsFractiorRateWhen Solving Any Problem In Percent, Remember The Following:Percent Problem Has 3 Elements: Base, Rate And Percentage.Percentage Is Part

How Did You Know That One Of Your Friends Walk Faster?

Determine Whether The Sides Or Angles Are Corresponding Sides, Corresponding Angles, Or Neither. 

II. Panuto: Hanapin At Bilugan Ang Mga Salitang Kasingkahulugan Ng Salitang "natatangi" Na NasaWord Search Box. Ang Mga Salitang Ito Ay Maaring Nakasulat Ng Pah

Batay Sa Sakong 7, Paano Maaring Maganap Ang Nais Ng Nagsasalita Sa Tula Na Di Pupulutin Sa Kangkungan Ang Pilipinas?

TOPIC: Doing Your Best In Everything That You Do.WRITE 4 SENTENCE PARAGRAPH. Ano Po And Present Na 4 Sentence Paragraph. And Then Po What Declarative, Imperativ

It Is A Selection Of Objects From A Set 

Pahelp Po,kailangan Na Po Kasi Ngayon,salamat Po

What Is Least Ten Scenarios That Depict Inequality In Yuor Community

What Are Used To Transform, Transfer Energy, Multiply Speed Or Force And Change The Direction Of The Force

How Are Cells Rows And Column Made

Nonsense = ReportCorrect Answer = Thanks(Heart), 5.0 Stars Vote, Follow

KAntoineDoixgo KAntoineDoixgo · Answer 1

✒️CIRCLE

[tex]••••••••••••••••••••••••••••••••••••••••••••••••••[/tex]

[tex] \large\underline{\mathbb{DIRECTIONS}:} [/tex]

Given the figure below, solve for the value of x.

[tex]••••••••••••••••••••••••••••••••••••••••••••••••••[/tex]

[tex] \large\underline{\mathbb{ANSWERS}:} [/tex]

[tex] \qquad \Large \rm{1) \; 15 \: units\:} [/tex]

[tex] \qquad \Large \rm{2) \; 20 \: units\:} [/tex]

[tex] \qquad \Large \rm{3) \; 52\degree\:} [/tex]

[tex] \qquad \Large \rm{4) \; 5 \: units\:} [/tex]

[tex] \qquad \Large \rm{5) \; 124 \degree\:} [/tex]

[tex]••••••••••••••••••••••••••••••••••••••••••••••••••[/tex]

[tex] \large\underline{\mathbb{SOLUTIONS}:} [/tex]

Number 1:

» Radius BA is perpendicular to tangent segment AC. Thus, ∆BAC is a right triangle. Find x using the Pythagorean theorem.

[tex] (BC)^2 = (BA)^2 + (AC)^2 [/tex]

[tex] (x)^2 = (9)^2 + (12)^2 [/tex]

[tex] x^2 = 81 + 144 [/tex]

[tex] x^2 = 225 [/tex]

[tex] \sqrt{x^2} = \sqrt{225} [/tex]

[tex] x = 15 [/tex]

[tex] \therefore [/tex] The length of segment x is 15 units

[tex] \: [/tex]

Number 2:

» Radius CQ is perpendicular to tangent segment QM. Thus, ∆CQM is a right triangle. Find x using the Pythagorean Theorem.

[tex] (QM)^2 + (CQ)^2 = (MC)^2 [/tex]

[tex] (x)^2 + (15)^2 = (25)^2 [/tex]

[tex] x^2 + 225 = 625 [/tex]

[tex] x^2 = 625 - 225 [/tex]

[tex] x^2 = 400 [/tex]

[tex] \sqrt{x^2} = \sqrt{400} [/tex]

[tex] x = 20 [/tex]

[tex] \therefore [/tex] The length of segment x is 20 units

[tex] \: [/tex]

Number 3:

» Angles T and S are supplementary. Thus, angles R and O are also supplementary.

[tex] m\angle R + m\angle O = 180\degree [/tex]

[tex] x + 128\degree = 180\degree [/tex]

[tex] x = 180\degree - 128\degree [/tex]

[tex] x = 52\degree [/tex]

[tex] \therefore [/tex] The measure of angle x is 52°

[tex] \: [/tex]

Number 4:

» Tangent segments AB and AD both drawn on circle C. Thus, their lengths are equal.

[tex] AB = AD [/tex]

[tex] 2x^2 + 4 = 54 [/tex]

[tex] 2x^2 = 54 - 4 [/tex]

[tex] 2x^2 = 50 [/tex]

[tex] \frac{\,2x^2\,}{2} = \frac{\,50\,}{2} \\ [/tex]

[tex] x^2 = 25 [/tex]

[tex] \sqrt{x^2} = \sqrt{25} [/tex]

[tex] x = 5 [/tex]

[tex] \therefore [/tex] The length of segment x is 5 units

[tex] \: [/tex]

» Angles Q and S are supplementary, Thus, angles R and A are also supplementary.

[tex] m\angle A + m\angle R = 180\degree [/tex]

[tex] m\angle A + 56\degree = 180\degree [/tex]

[tex] m\angle A = 180\degree - 56\degree [/tex]

[tex] m\angle A = 124\degree [/tex]

» The measure of a central angle subtended by the two radii is equal to its intercepted arc.

[tex] m\overset{\frown}{QS} = m\angle A [/tex]

[tex] x = 124\degree [/tex]

[tex] \therefore [/tex] The measure of the arc x is 124°

[tex]••••••••••••••••••••••••••••••••••••••••••••••••••[/tex]

(ノ^_^)ノ